With ballots set to go out this week, Democrat Jay Inslee and Republican Rob McKenna sparred Tuesday night over education funding, immigration and transportation in their last debate of the governor’s race.

The rivals traded jabs about each other’s proposals, delving deeper into issues and at times getting personal during the hourlong debate, the fifth in a race that is considered one of the most competitive gubernatorial contests in the country.

Each candidate touted his plan for increasing education funding without raising taxes.

Inslee, a former congressman from Bainbridge Island, wants to cut health-care costs and grow the economy, bringing in more money for schools. McKenna, the state attorney general, wants to cap spending in the rest of the budget and shift any extra revenue to education.

McKenna said he would bring a new culture and a “fresh crew” to a state government that has not had a Republican governor in 28 years. Inslee said he would require every state employee to be trained in “lean management” techniques, which he says would make government more effective.

But the most heated exchanges came while discussing a property-tax-swap proposal embraced by McKenna. The idea, originally pitched by Democratic and Republican lawmakers, would simultaneously reduce local school levies and increase the state levy.

The idea has been proposed in response to a state Supreme Court ruling that the state isn’t adequately funding public schools and relies too heavily on local property taxes.

Inslee has called the idea a gimmick that would not generate new money but would raise property taxes in more affluent districts, although it would reduce taxes in other districts.

“It may help Olympia politicians on paper; it does not help students in school,” Inslee said.

In response, McKenna cited newspaper accounts calling Inslee’s attacks misleading and saying the plan is a reasonable way to increase predictability in education funding. The Republican added that Inslee doesn’t have a plan.

“Your premise is false, Jay,” McKenna said. “You just keep repeating it because you hope by repetition it will just fool people into believing it.”

At another point, McKenna and Inslee talked over each other while arguing about a website Inslee put up about the tax swap.

It was that kind of night for the candidates, who are battling to succeed Democratic Gov. Chris Gregoire.

Tuesday’s debate, sponsored by The Seattle Times and KING 5, was the candidates’ last high-profile chance to address voters.

On some issues, they were more detailed than in the past.

Asked which tax loopholes they would consider closing, Inslee cited one related to the sale of bull semen and another that helps the fossil-fuel industry. He said he would support making all loopholes come up for regular review.

McKenna said he wants to work to end tax breaks that go to online and out-of-state retailers.

Both said they would support continuing breaks that benefit Microsoft.

On immigration, McKenna said he would require people to show proof of citizenship before getting a driver’s license. If they don’t have proof, he said, applicants should only get a driver’s permit that can’t be used as official identification.

Inslee said he does not support that idea.

McKenna said he also wants to reduce fraud in the Department of Social and Health Services by requiring food-stamp cards to have a photograph. Inslee said he would make the department more efficient.

Both candidates said they would work while in office on a package to get more funding to address transportation issues, including perhaps more tolling.

Given the opportunity to ask a question of Inslee, McKenna asked why he thinks 10 daily newspapers had endorsed the Republican and none yet had endorsed the Democrat.

“I don’t work for the newspapers of the state of Washington,” Inslee said. “I work for the people of the state of Washington.”

In his question, Inslee asked McKenna what he has done to further women’s abortion rights.

“The premise of the question is false,” McKenna said, noting that he respects current state law giving women the right to choose.

In closing statements, the candidates summarized arguments they have made throughout the campaign.

Inslee described his jobs plan, which he says is unique to Washington.

“We are the most innovative people in America,” he said, “perhaps the world.”

McKenna touted his bipartisan endorsements and ended with a spin on the classic political question of “are you better off than you were four years ago?”

“Do you think that you’ll be better off four years from now if we put the same people back in charge of Olympia that have been running it the past 28 years?” he asked.

Both campaigns are preparing for a homestretch that should include a lot of spending. On Tuesday, the Republican Governors Association announced it was putting $3 million more into independent expenditures for McKenna. That brought the group’s total to $11.3 million.

A pro-Inslee group has raised $7.9 million. The campaigns each have raised about $10 million.